| 1 | 1 | 1 | 1 | |||||
limn→∞ ( | + | + | +...+ | ) | ||||
| 2 * 4 | 5 * 7 | 8 * 10 | (3n−1)(3n+1) |
| 1 | 1 | 1 | 1 | ||||
= | ( | − | ), niestety nic nie daje rozkład na ułamki | ||||
| (3k−1)(3k+1) | 2 | 3k−1 | 3k+1 |
| 1 | π | ||
(1 − | ) | ||
| 2 | 3√3 |
| 1 | 1 | |||
∑n=1∞ | = | ∫01∑n=1∞(x3n−2 − x3n) dx = | ||
| (3n−1)(3n+1) | 2 |
| 1 | 1+x | 1 | π | |||||
= | ∫01 | dx = | (1− | ) | ||||
| 2 | 1+x+x2 | 2 | 3√3 |